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Related Concept Videos

Transition State Theory01:25

Transition State Theory

Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
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Criterion for explosive percolation transitions on complex networks.

Hans Hooyberghs1, Bert Van Schaeybroeck

  • 1Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. hans.hooyberghs@fys.kuleuven.be

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 27, 2011
PubMed
Summary

Explosive phase transitions on complex networks occur when the mean cluster size diverges before the percolation threshold. This indicates that network growth, not proportional to size, triggers explosive percolation.

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Area of Science:

  • Complex networks
  • Statistical physics
  • Network science

Background:

  • Friedman and Landsberg previously explored explosive phase transitions in complex networks.
  • Understanding the conditions for explosive transitions is crucial for network analysis.

Purpose of the Study:

  • To extend the understanding of explosive phase transitions on complex networks.
  • To identify general conditions leading to explosive percolation transitions.

Main Methods:

  • Analysis of cluster-size distribution.
  • Theoretical deduction based on network properties.
  • Simulations and analytical calculations on various network models.

Main Results:

  • Explosive percolation occurs if the mean number of nodes per cluster diverges before the transition threshold.
  • A key condition is that the number of clusters does not grow proportionally with network size.
  • Findings supported by simulations and analytical derivations.

Conclusions:

  • The study provides a generalized condition for explosive percolation transitions.
  • Network size and cluster distribution dynamics are critical factors.
  • The findings offer deeper insights into phase transitions in complex systems.